Invariant submanifolds of contact (, )-manifolds are studied. Our main result is that any invariant submanifold of a non-Sasakian contact (, )-manifold is always totally geodesic and, conversely, every totally geodesic submanifold of a non-Sasakian contact (, )-manifold, 0, such that the characteristic vector field is tangent to the submanifold is invariant. Some consequences of these results are then discussed.
Invariant submanifolds of contact (k,μ)-manifolds
CAPPELLETTI MONTANO, BENIAMINO;
2008
Abstract
Invariant submanifolds of contact (, )-manifolds are studied. Our main result is that any invariant submanifold of a non-Sasakian contact (, )-manifold is always totally geodesic and, conversely, every totally geodesic submanifold of a non-Sasakian contact (, )-manifold, 0, such that the characteristic vector field is tangent to the submanifold is invariant. Some consequences of these results are then discussed.
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